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At least 1,261 records · Page 70

Make the Fastest Faster: Importance Mask Synthesis for Interactive Volume Visualization using Reconstruction Neural Networks

Visualizing a large-scale volumetric dataset with high resolution is challenging due to the substantial computational time and space complexity. Recent deep learning-based image inpainting methods significantly improve rendering latency by reconstructing a high-resolution image for visualization in constant time on GPU from a partially rendered image where only a portion of pixels go through the expensive rendering pipeline. However, existing solutions need to render every pixel of either a predefined regular sampling pattern or an irregular sample pattern predicted from a low-resolution image rendering. Both methods require a significant amount of expensive pixel-level rendering. In this work, we provide Importance Mask Learning (IML) and Synthesis (IMS) networks, which are the first attempts to directly synthesize important regions of the regular sampling pattern from the user’s view parameters, to further minimize the number of pixels to render by jointly considering the dataset, user behavior, and the downstream reconstruction neural network. Our solution is a unified framework to handle various types of inpainting methods through the proposed differentiable compaction/decompaction layers. Experiments show our method can further improve the overall rendering latency of state-of-the-art volume visualization methods using reconstruction neural network for free when rendering scientific volumetric datasets. Our method can also directly optimize the off-the-shelf pre-trained reconstruction neural networks without elongated retraining.

Large-scale data↗

B-DeepONet: An enhanced Bayesian DeepONet for solving noisy parametric PDEs using accelerated replica exchange SGLD

Here, the Deep Operator Network (DeepONet) is a neural network architecture used to approximate operators, including the solution operator of parametric PDEs. DeepONets have shown remarkable approximation ability. However, the performance of DeepONets deteriorates when the training data is polluted with noise, a scenario that occurs in practice. To handle noisy data, we propose a Bayesian DeepONet based on replica exchange Langevin diffusion (reLD). Replica exchange uses two particles. The first particle trains a DeepONet to exploit the loss landscape and make predictions. The other particle trains a different DeepONet to explore the loss landscape and escape local minima via swapping. Compared to DeepONets trained with state-of-the-art gradient-based algorithms (e.g., Adam), the proposed Bayesian DeepONet greatly improves the training convergence for noisy scenarios and accurately estimates the uncertainty. To further reduce the high computational cost of the reLD training of DeepONets, we propose (1) an accelerated training framework that exploits the DeepONet's architecture to reduce its computational cost up to 25% without compromising performance and (2) a transfer learning strategy that accelerates training DeepONets for PDEs with different parameter values. Finally, we illustrate the effectiveness of the proposed Bayesian DeepONet using four parametric PDE problems.

97 MATHEMATICS AND COMPUTING↗

ReLU, Sparseness, and the Encoding of Optic Flow in Neural Networks

Accurate self-motion estimation is critical for various navigational tasks in mobile robotics. Optic flow provides a means to estimate self-motion using a camera sensor and is particularly valuable in GPS- and radio-denied environments. The present study investigates the influence of different activation functions—ReLU, leaky ReLU, GELU, and Mish—on the accuracy, robustness, and encoding properties of convolutional neural networks (CNNs) and multi-layer perceptrons (MLPs) trained to estimate self-motion from optic flow. Our results demonstrate that networks with ReLU and leaky ReLU activation functions not only achieved superior accuracy in self-motion estimation from novel optic flow patterns but also exhibited greater robustness under challenging conditions. The advantages offered by ReLU and leaky ReLU may stem from their ability to induce sparser representations than GELU and Mish do. Our work characterizes the encoding of optic flow in neural networks and highlights how the sparseness induced by ReLU may enhance robust and accurate self-motion estimation from optic flow.

97 MATHEMATICS AND COMPUTING↗

Techno-economic implications and cost of forecasting errors in solar PV power production using optimized deep learning models

Accurate solar Photovoltaic (PV) power forecasting is important for enhancing both the performance and economic feasibility of PV systems. This study evaluates several deep learning models, including Dense Neural Networks (DNN), Long Short-Term Memory (LSTM), Convolutional Neural Networks (CNN), and a hybrid LSTMCNN model, for predicting PV power production one day in advance. Prior to optimization, the models exhibited relatively high errors, with the best model (DNN) achieving a Root Mean Square Error (RMSE) of 31.13 kW and a coefficient of determination (R 2 ) of 62.15 %. After employing Bayesian optimization, the LSTM-CNN model demonstrated the best performance, with the RMSE reduced to 9.79 kW and R 2 improved to 97.62 %, showcasing significant enhancement in predictive accuracy. Here, the economic evaluation considered three cases: rewards for underestimation (0.08 USD/kWh), no rewards, and penalties for both over-and underestimation (120 % of the utility tariff). In the rewards scenario, the LSTM-CNN model reduced the Levelized Cost of Electricity (LCOE) by 4 %, while in the penalty scenario, a backup diesel generator would have increased the LCOE by 49 %. Additionally, the LSTM-CNN model minimized financial losses, achieving the lowest penalties and maximizing net cash flow compared to other models, demonstrating its overall technical and economic superiority.

Deep learning↗

Optimization-based control using input convex neural networks

Input convex neural networks (ICNNs) are a family of deep learning models where the outputs are constructed to be convex functions of the inputs. By parameterizing system models using ICNNs, optimization-based control problems can be solved as convex optimization problems, leading to improved performance and robustness. This work proposes a novel framework where the control objective function and constraints are modelled using ICNNs. A case study of optimization-based control with output constraints is conducted on a process with input multiplicity and nonminimum phase behavior. The simulation results demonstrate improved economic yield compared with normal neural networks. Additionally, the input convexity formulation is compared with simple regularization techniques, and unique benefits such as improved data efficiency and robustness of the proposed formulation are shown. Finally, by explicitly incorporating prior knowledge about convexity, this framework provides a good balance between the universal approximation power of deep learning and computational feasibility required by control.

42 ENGINEERING↗

DLSIA: Deep Learning for Scientific Image Analysis

DLSIA (Deep Learning for Scientific Image Analysis) is a Python-based machine learning library that empowers scientists and researchers across diverse scientific domains with a range of customizable convolutional neural network (CNN) architectures for a wide variety of tasks in image analysis to be used in downstream data processing. DLSIA features easy-to-use architectures, such as autoencoders, tunable U-Nets and parameter-lean mixed-scale dense networks (MSDNets). Additionally, this article introduces sparse mixed-scale networks (SMSNets), generated using random graphs, sparse connections and dilated convolutions connecting different length scales. For verification, several DLSIA-instantiated networks and training scripts are employed in multiple applications, including inpainting for X-ray scattering data using U-Nets and MSDNets, segmenting 3D fibers in X-ray tomographic reconstructions of concrete using an ensemble of SMSNets, and leveraging autoencoder latent spaces for data compression and clustering. As experimental data continue to grow in scale and complexity, DLSIA provides accessible CNN construction and abstracts CNN complexities, allowing scientists to tailor their machine learning approaches, accelerate discoveries, foster interdisciplinary collaboration and advance research in scientific image analysis.

97 MATHEMATICS AND COMPUTING↗

Machine-Learning-based Algorithms for Automated Image Segmentation Techniques of Transmission X-ray Microscopy (TXM)

Four state-of-the-art Deep Learning-based Convolutional Neural Networks (DCNN) were applied to automate the semantic segmentation of a 3D Transmission x-ray Microscopy (TXM) nanotomography image data. The standard U-Net architecture as baseline along with UNet++, PSPNet, and DeepLab v3+ networks were trained to segment the microstructural features of an AA7075 micropillar. A workflow was established to evaluate and compare the DCNN prediction dataset with the manually segmented features using the Intersection of Union (IoU) scores, time of training, confusion matrix, and visual assessment. Comparing all model segmentation accuracy metrics, it was found that using pre-trained models as a backbone along with appropriate training encoder-decoder architecture of the Unet++ can robustly handle large volumes of x-ray radiographic images in a reasonable amount of time. This opens a new window for handling accurate and efficient image segmentation of in situ time-dependent 4D x-ray microscopy experimental datasets.

36 MATERIALS SCIENCE↗

Building thermal dynamics modeling with deep transfer learning using a large residential smart thermostat dataset

Understanding thermal dynamics and obtaining the computational model of residential buildings enable its scaled application in energy retrofits, control optimization and decarbonization. In this paper, we present a deep learning approach to model building thermal dynamics with smart thermostat data collected from residential buildings, with the goal to investigate model generalizability. In the first stage, we developed and compared different Deep Learning architectures including Convolutional Neural Networks (CNN), Long Short-Term Memory (LSTM) models and CNN-LSTM to predict indoor air temperature in a multi-step time horizon. In the second stage, we implemented a Transfer Learning (TL) process, which aims to improve the prediction performance on a new set of buildings (targets), exploiting the knowledge of related or similar buildings (sources). Different TL strategies and source model identification methods were investigated. The study showed that the CNN-LSTM performed the best among the architectures compared, with an average Mean Absolute Error (MAE) of 0.26 °C for one-hour-ahead (twelve 5-min future steps) predictions. Furthermore, the results showed that freezing the LSTM layer and fine-tuning the other layers of the CNN-LSTM achieved the best performance among four TL strategies, which further improved the performance with respect to a machine learning approach by 10%, and proving the effectiveness and generalizability of the proposed approach. A comparison of three different source model identification methods showed that randomly selecting source models constrained by similar building characteristics can provide good TL performance while retaining simplicity comparing with other quantitative source identification methods.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Multi phenomena melt pool sensor data fusion for enhanced process monitoring of laser powder bed fusion additive manufacturing

Finding actionable trends in laser-based metal additive manufacturing process monitoring data is challenging owing to the diversity and complexity of the underlying physical interactions. A single monitoring solution that captures a particular process phenomenon, such as a photodiode that tracks melt pool intensity, is not alone capable of evaluating process stability or detecting flaw formation with sufficient precision for routine application in industry. In this work, to improve flaw detection performance, we adopted a data fusion approach that captures multiple process phenomena. To demonstrate this, we acquired data from laser powder bed fusion (LPBF) builds of cylindrical specimens produced with different laser spot sizes, emulating defocusing due to process faults such as thermal lensing. The resulting specimens had porosity of varying types and severity, quantified by post-build non-destructive X-ray computed tomography, Archimedes density measurements, and destructive metallographic characterization. During the build, the melt pool state was monitored with two coaxial high-speed video cameras and a temperature field imaging system. Physically intuitive low-level melt pool signatures, such as melt pool temperature, shape and size, and spatter intensity were extracted from this high-dimensional, image-based sensor data. These process signatures were subsequently used as input features in relatively simple machine learning models, such as a support vector machine, which were trained to detect laser defocusing, and in addition, predict porosity type and severity. The results show that the data fusion approach significantly enhanced system performance by reducing the overall false positive rate from ~ 0.1 to ~ 0.001 without sacrificing the true positive rate (~0.90). These results were at par with a black-box, deep machine learning approach (convolutional neural network).

36 MATERIALS SCIENCE↗

Search for two-neutrino double-beta decay of 136 Xe to the $0$$^{+}_{1}$ excited state of 136 Ba with the complete EXO-200 dataset*

A new search for two-neutrino double-beta (2νββ) decay of 136 Xe to the $0$$^{+}_{1}$ excited state of 136 Ba is performed with the full EXO-200 dataset. A deep learning-based convolutional neural network is used to discriminate signal from background events. Signal detection efficiency is increased relative to previous searches by EXO-200 by more than a factor of two. With the addition of the Phase II dataset taken with an upgraded detector, the median 90% confidence level half-life sensitivity of 2νββ decay to the $0$$^{+}_{1}$ state of 136 Ba is 2.9 x 10 24 yr using a total 136 Xe exposure of 234.1 kg yr. Furthermore, no statistically significant evidence for 2νββ decay to the $0$$^{+}_{1}$ state is observed, leading to a lower limit of $T$$^{2v}_{1/2}$(0 + → $0$$^{+}_{1}$) > 1.4 x 10 24 yr at 90% confidence level, improved by 70% relative to the current world's best constraint.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Fraction of broad absorption line quasars in different radio morphologies

ABSTRACT In this study, we investigated the orientation model of Broad Absorption Line (BAL) quasars using a sample of sources that are common in Sloan Digital Sky Survey (SDSS) Data Release (DR)-16 quasar catalogue and Very Large Array (VLA)-Faint Images of the Radio Sky at Twenty Centimeters (FIRST) survey. Using the radio cut-out images from the FIRST survey, we first designed a deep-learning model using convolutional neural networks (CNN) to classify the quasar radio morphologies into the core-only, young jet, single lobe, or triples. These radio morphologies are further sub-classified into core-dominated and lobe-dominated sources. The CNN models can classify the sources with a high precision of >98 ${{\ \rm per\ cent}}$ for all the morphological sub-classes. The average BAL fraction in the resolved core, core-dominated, and lobe-dominated quasars are consistent with the BAL fraction inferred from radio and infrared surveys. We also present the distribution of BAL quasars as a function of quasar orientation by using the radio core-dominance as an orientation indicator. A similar analysis is performed for HiBALs, LoBALs, and FeLoBALs. All the radio morphological sub-classes and BAL sub-classes show an increase in BAL fraction at high orientation angles of the jets with respect to the line of sight. Our analysis suggests that BAL quasars are more likely to be found in viewing angles close to the equatorial plane of the quasar. However, a pure orientation model is inadequate, and a combination of orientation and evolution is probably the best way to explain the complete BAL phenomena.

79 ASTRONOMY AND ASTROPHYSICS↗

Mitigating Catastrophic Forgetting in Deep Learning in a Streaming Setting Using Historical Summary

Recent advancements in scientific equipment and the adaptation of electronics and the Internet of Things (IoT) in our everyday lives resulted in large and complex data production at a high rate. Making meaningful and timely knowledge discovery at a modest cost from this big data is difficult for computing power and storage limitations. Training deep learning models incrementally in a streaming setting can help us with overcoming these limitations. However, in a well-known phenomenon named catastrophic forgetting, incrementally trained models increasingly perform poorly on the past data. To mitigate catastrophic forgetting in training in a streaming setting, we propose constructing a historical summary over time and use the summary with newly arrived data during incremental training. We propose various data summarization techniques such as random sampling, micro clustering, coreset computation, and Auto Encoders to counteract catastrophic forgetting. We built a pipeline for incremental training with a historical summary for training deep learning models for streaming data. We demonstrate the effectiveness of historical summary in mitigating catastrophic forgetting using three case studies involving three different deep learning applications: an Artificial Neural Network (ANN) for classification task on MNIST dataset, a language model (RNN-LM) on the WikiText2 dataset, and a Convolutional Neural Network (CNN), ResNet50 to classify the ImageNet dataset. Through the training of the models, we observe that catastrophic forgetting is evident in ANN and CNN but not in an RNN. For the first task, our method recovers up to 47.9% lost accuracy due to catastrophic forgetting. For the third task, the historical summary recovers classification accuracy by up to 25%. For the second task, though there is not proof of catastrophic forgetting, the training performance (PPL) improves by up to 26% with historical summary.

Dash, Sajal↗

PowerMappeR: Power-Optimized Mapping of SNNs onto ReRAM Crossbars coupled via Packet-Switched NoCs

Many recent efforts in developing hardware-accelerated spiking neural networks (SNNs) are characterized by deep co-design between algorithms, architectures, and devices. Architectural advances overcome device constraints by coupling together many small resistive-RAM (ReRAM) crossbars via a network-on-chip (NoC) for neuromorphic component operation. Concurrently, improved SNN training methods increase accuracy and structural sparsity in networks despite growing problem sizes. Finally, compilers leverage these attributes to minimize area and inter-crossbar communication while mapping large SNNs to sophisticated architectures. However, for compiler-driven co-design to realize increasingly complex and profitable optimizations, a compile-time view of power consumption is critical. We present PowerMappeR to express and optimize over mapping-, architecture-, and device-specific power consumption information. By modeling the dynamic power of well-established components, we develop an integer linear programming (ILP)-based, encoding-agnostic, parametric power estimation model. Using this model, we demonstrate practical improvements in area and inter-crossbar communication by 0%–9.5% and 1.4%–5.1%, respectively. We also limit hotspot formation during optimization, achieving comparable or better results in targeted metrics with up to 96.4%–97.1% restriction of hotspot magnitude. Finally, we introduce profile-guided formulations to reduce worst-case and expected-case hotspot magnitude by 40.7%–69.5% and 40.6%–56.3%, respectively. Optimizing worst-case hotspot magnitude incidentally improves expected-case magnitude by 10.85%–33.45%. Reciprocally, optimizing expected-case magnitude incidentally improves worst-case magnitude by 4.33%–39.87%. Validation against hardware simulators confirms that PowerMappeR can decrease dynamic power consumption by 12.6%–27.3%.

Pohl, Devin [ORNL] (ORCID:0009000040149027)↗

Applications of Nickelate perovskites for neuromorphic computing from electronic structure and Machine Learning

While the limit of Moore's law is presently being reached with current microelectronic technologies, we need to develop new paradigms that overcome this limitation. In that respect, neuromorphic computing is a concept that emulates the neural behavior and response of the human brain, and it has been recognized as a promising alternative approach. In this research project, we will perform multi-fidelity scale bridging to explore the potential use of materials with metal to insulator transition for neuromorphic applications. In particular, rare earth nickelates are promising for such purposes, as the transition in these materials is quite sensitive to a broad set of different external stimuli. Our multi-fidelity approach will bridge the high-fidelity electronic structure calculations with classical potentials. We will bridge dynamical mean field theory with a classical atomistic representation via a deep learning force field. The neural network is trained with energies, charges, and forces obtained by accurate electronic structure theories based on Dynamical Mean Field Theory. The configurational space is generated from known crystal phases, ab initio molecular dynamics with exchange-correlation functionals corrected with the Hubbard model, disordered phases with different concentrations of oxygen vacancies, and nonsymmetrical positions and induced strain by grain interfaces or contact with a substrate. Strategies to train the model with a reduced number of training examples are obtained from active learning methods, and new structures for improving the learning process are generated by using machine learning autoencoders. This classical potential will be validated through a diversity of electronic structure methods and represents an important step to combine the flexibility and accuracy of first-principles with the speed of classical potentials. The generated multi-fidelity surrogate model will be used to understand the role of strain, oxygen vacancies, proton doping, the variation of the crystal phase, substrate effects, vibrational effects as the octahedral rotation, grain boundaries and defect effects on the response of a Metal to Insulator Transition (MIT) in correlated materials. Long time and large-scale simulations will help understand the role of different stimuli to control the hysteresis of the MIT, as it has been experimentally suggested. Selected configurations will be analyzed with higher-level theories to provide an accurate electronic description and to study how the orbitals and charges are rearranged under different conditions.

36 MATERIALS SCIENCE↗

Classifying Seyfert Galaxies with Deep Learning

The traditional classification for a subclass of the Seyfert galaxies is visual inspection or using a quantity defined as a flux ratio between the Balmer line and forbidden line. One algorithm of deep learning is the convolution neural network (CNN), which has shown successful classification results. We build a one-dimensional CNN model to distinguish Seyfert 1.9 spectra from Seyfert 2 galaxies. We find that our model can recognize Seyfert 1.9 and Seyfert 2 spectra with an accuracy of over 80% and pick out an additional Seyfert 1.9 sample that was missed by visual inspection. We use the new Seyfert 1.9 sample to improve the performance of our model and obtain a 91% precision of Seyfert 1.9. These results indicate that our model can pick out Seyfert 1.9 spectra among Seyfert 2 spectra. We decompose the Hα emission line of our Seyfert 1.9 galaxies by fitting two Gaussian components and derive the line width and flux. We find that the velocity distribution of the broad Hα component of the new Seyfert 1.9 sample has an extending tail toward the higher end, and the luminosity of the new Seyfert 1.9 sample is slightly weaker than the original Seyfert 1.9 sample. This result indicates that our model can pick out the sources that have a relatively weak broad Hα component. In addition, we check the distributions of the host galaxy morphology of our Seyfert 1.9 samples and find that the distribution of the host galaxy morphology is dominated by a large bulge galaxy. In the end, we present an online catalog of 1297 Seyfert 1.9 galaxies with measurements of the Hα emission line.

79 ASTRONOMY AND ASTROPHYSICS↗

Advances in Hyperspectral Image Classification Methods for Vegetation and Agricultural Cropland Studies

Hyperspectral data are becoming more widely available via sensors on airborne and unmanned aerial vehicle (UAV) platforms, as well as proximal platforms. While space-based hyperspectral data continue to be limited in availability, multiple spaceborne Earth-observing missions on traditional platforms are scheduled for launch, and companies are experimenting with small satellites for constellations to observe the Earth, as well as for planetary missions. Land cover mapping via classification is one of the most important applications of hyperspectral remote sensing and will increase in significance as time series of imagery are more readily available. However, while the narrow bands of hyperspectral data provide new opportunities for chemistry-based modeling and mapping, challenges remain. Hyperspectral data are high dimensional, and many bands are highly correlated or irrelevant for a given classification problem. For supervised classification methods, the quantity of training data is typically limited relative to the dimension of the input space. The resulting Hughes phenomenon, often referred to as the curse of dimensionality, increases potential for unstable parameter estimates, overfitting, and poor generalization of classifiers. This is particularly problematic for parametric approaches such as Gaussian maximum likelihood–based classifiers that have been the backbone of pixel-based multispectral classification methods. This issue has motivated investigation of alternatives, including regularization of the class covariance matrices, ensembles of weak classifiers, development of feature selection and extraction methods, adoption of nonparametric classifiers, and exploration of methods to exploit unlabeled samples via semi-supervised and active learning. Data sets are also quite large, motivating computationally efficient algorithms and implementations. This chapter provides an overview of the recent advances in classification methods for mapping vegetation using hyperspectral data. Three data sets that are used in the hyperspectral classification literature (e.g., Botswana Hyperion satellite data and AVIRIS airborne data over both Kennedy Space Center and Indian Pines) are described in Section 3.2 and used to illustrate methods described in the chapter. An additional high-resolution hyperspectral data set acquired by a SpecTIR sensor on an airborne platform over the Indian Pines area is included to exemplify the use of new deep learning approaches, and a multiplatform example of airborne hyperspectral data is provided to demonstrate transfer learning in hyperspectral image classification. Classical approaches for supervised and unsupervised feature selection and extraction are reviewed in Section 3.3. In particular, nonlinearities exhibited in hyperspectral imagery have motivated development of nonlinear feature extraction methods in manifold learning, which are outlined in Section 3.3.1.4. Spatial context is also important in classification of both natural vegetation with complex textural patterns and large agricultural fields with significant local variability within fields. Approaches to exploit spatial features at both the pixel level (e.g., co-occurrence–based texture and extended morphological attribute profiles [EMAPs]) and integration of segmentation approaches (e.g., HSeg) are discussed in this context in Section 3.3.2. Recently, classification methods that leverage nonparametric methods originating in the machine learning community have grown in popularity. An overview of both widely used and newly emerging approaches, including support vector machines (SVMs), Gaussian mixture models, and deep learning based on convolutional neural networks is provided in Section 3.4. Strategies to exploit unlabeled samples, including active learning and metric learning, which combine feature extraction and augmentation of the pool of training samples in an active learning framework, are outlined in Section 3.5. Integration of image segmentation with classification to accommodate spatial coherence typically observed in vegetation is also explored, including as an integrated active learning system. Exploitation of multisensor strategies for augmenting the pool of training samples is investigated via a transfer learning framework in Section 3.5.1.2. Finally, we look to the future, considering opportunities soon to be provided by new paradigms, as hyperspectral sensing is becoming common at multiple scales from ground-based and airborne autonomous vehicles to manned aircraft and space-based platforms.

Pasolli, Edoardo↗

hippynn Python Package

hippynn is a python package for defining, training, and applying neural networks to atomistic systems. In particular, it focuses on Hierarchical Interacting Particle Neural Networks (HIP-NNs), a deep learning architecture for atomistic systems. HIP-NNs take input data describing the properties of atomistic systems (often generated using ab-initio quantum mechanics) to learn fast and accurate models. A trained HIP-NN can predict potential energy surfaces, atomic charges, and more. hippynn uses PyTorch for portable high-performance code, including both CPU and GPU support. hippynn allows for extensive customization, including user-defined models and loss functions, to facilitate future research into extensions of HIP-NN as well as other atomistic deep learning models.

Lubbers, Nicolas↗

Neural-network learning of SPOD latent dynamics

Here, we aim to reconstruct the latent space dynamics of high dimensional, quasi-stationary systems using model order reduction via the spectral proper orthogonal decomposition (SPOD). The proposed method is based on three fundamental steps: in the first, once that the mean flow field has been subtracted from the realizations (also referred to as snapshots), we compress the data from a high-dimensional representation to a lower dimensional one by constructing the SPOD latent space; in the second, we build the time-dependent coefficients by projecting the snapshots containing the fluctuations onto the SPOD basis and we learn their evolution in time with the aid of recurrent neural networks; in the third, we reconstruct the high-dimensional data from the learnt lower -dimensional representation. The proposed method is demonstrated on two different test cases, namely, a compressible jet flow, and a geophysical problem known as the Madden-Julian Oscillation. An extensive comparison between SPOD and the equivalent POD-based counterpart is provided and differences between the two approaches are highlighted. The numerical results suggest that the proposed model is able to provide low rank predictions of complex statistically stationary data and to provide insights into the evolution of phenomena characterized by specific range of frequencies. The comparison between POD and SPOD surrogate strategies highlights the need for further work on the characterization of the interplay of error between data reduction techniques and neural network forecasts.

97 MATHEMATICS AND COMPUTING↗